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Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations. (English) Zbl 1236.65091
A formula for integrals (primitives) of Bernstein polynomials in terms of sums of Bernstein polynomials is given. For a very special class of $2m$th order linear ordinary differential equations, subject to Dirichlet boundary conditions, a numerical approximation method is proposed by integrating the differential equation $2m$-times and using Bernstein polynomials as basis functions for a Galerkin method. The above-mentioned formula for integrals of Bernstein polynomials is used to calculate the corresponding matrix elements. Some numerical examples illustrate the approach.

65L10Boundary value problems for ODE (numerical methods)
34B05Linear boundary value problems for ODE
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65D30Numerical integration
Full Text: DOI
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